Advantages of ROOTING your phone

Root allows you run as "superuser", effectively giving you total control over the OS. You can add/remove stuff from the device memory, change ROMS, recovery images, themes, backup installed apps.... A nice round-up of some useful reading can be found here.

I've heard that getting root removes the ability to install paid-for Market apps; can that be true?

I find it hard to believe, that just creating a setuid-root /bin/su could do that, but I don't know. Or was that referring to booting specific ROMs, not just getting root and then booting the original ROM?

any other downsides of getting root? real ones, that is, not the jokey ones in the links?